7,913 research outputs found
On an open problem of characterizing the birationality of 4K
We answer an open problem raised by Chen and Zhang in 2008 and prove that,
for any minimal projective 3-fold of general type with the geometric genus
, is birationally fibred by a pencil of -surfaces (i.e.
, ) if and only if the -canonical map is
non-birational. The statement does not hold for those with the geometric genus
according to our examples.Comment: 11 page
Coevolution of game and network structure: The temptation increases the cooperator density
Most papers about the evolutionary game on graph assume the statistic network
structure. However, social interaction could change the relationship of people.
And the changing social structure will affect the people's strategy too. We
build a coevolutionary model of prisoner's dilemma game and network structure
to study the dynamic interaction in the real world. Based on the asynchronous
update rule and Monte Carlo simulation, we find that, when players prefer to
rewire their links to the richer, the cooperation density will increase. The
reason of it has been analyzed.Comment: 7 pages, 6 figure
Thermodynamic fluctuation in black string flow
It has long been noticed that Laudau-Lifshitz theory can be used to study the
fluctuation of a system that contains a black hole. Since the black string can
be constructed by extending n-dimensional black hole into one extra dimension.
We study the fluctuation of black string flow with a Schwarzschlid-like metric
in D=n+1 dimensional spacetime and a charged solution in D=5 dimensional
spacetime and get the second moments of the fluctuation of the mass flux and
charge flux
Quantum-Inspired Gravitational Wave Detector
A new gravitational-wave detector, which is devised based on quantum weak
measurement amplification, is introduced and shown has the potential to
significantly improve the strain sensitivity of gravitational-wave detection.Comment: Essay written for the Gravity Research Foundation 2018 Awards for
Essays on Gravitation, Comments are welcome
Resonances Driven by a Neutrino Gyroscope and Collective Neutrino Oscillations in Supernovae
We show that flavor evolution of a system of neutrinos with continuous energy
spectra as in supernovae can be understood in terms of the response of
individual neutrino flavor-isospins (NFIS's) to the mean field. In the case of
a system initially consisting of nu_e and anti-nu_e with the same energy
spectrum but different number densities, the mean field is very well
approximated by the total angular momentum of a neutrino gyroscope. Assuming
that NFIS evolution is independent of the initial neutrino emission angle, the
so-called single-angle approximation, we find that the evolution is governed by
two types of resonances driven by precession and nutation of the gyroscope,
respectively. The net flavor transformation crucially depends on the
adiabaticity of evolution through these resonances. We show that the results
for the system of two initial neutrino species can be extended to a system of
four species with the initial number densities of nu_e and anti-nu_e
significantly larger than those of nu_x and anti-nu_x. Further, we find that
when the dependence on the initial neutrino emission angle is taken into
account in the multi-angle approximation, nutation of the mean field is quickly
damped out and can be neglected. In contrast, precession-driven resonances
still govern the evolution of NFIS's with different energy and emission angles
just as in the single-angle approximation. Our pedagogical and analytic study
of collective neutrino oscillations in supernovae provides some insights into
these seemingly complicated yet fascinating phenomena.Comment: 41 pages, 20 figures, to appear in Physical Review
Intrinsic-Correlation Quantum Key Generation
A new conceptual key generation scheme is presented by using intrinsic
quantum correlations of single photons between Alice and Bob. The intrinsic
bi-partite correlation functions allow key bit to be generated through high
level communication language i.e. a key bit is directly encoded to shared
correlation functions not to the state and detection of a photon at Bob does
not mean key bit. These make the scheme robust against intercept-resend attack
because Alice and Bob can always check the errors in their measurements and
reveal the presence of Eve in their channel without leaking any key bit
information. The laser source is located in the middle of Alice and Bob,
consists of two modes (x,y), relatively random phase-modulated weak coherent states combined in a perfect 50/50 beam splitter.
The scheme is strictly relied on the perfect beam splitter and mean photon
number less than 1, where more than one photon in a coherent pulse will
introduce more errors in Bob even without the presence of Eve. From the
percentage of errors in Bob, we can estimate the amount of information will be
leaked to Eve in the photon-number splitting attack. This scheme can preserve
the randomness of phase-randomized light source for doubling the communication
distance as in original Ekert's protocol and providing the raw key generation
rate a factor of 2 higher than weak coherent light protocols.Comment: 13 pages, 1 figure, 1 tabl
On projective 3-folds of general type with small positive geometric genus
In this paper we study pluricanonical maps of minimal projective 3-folds of
general type with geometric genus , and . We go in the direction
pioneered by Enriques and Bombieri, and other authors, pinning down, for low
projective genus, a finite list of exceptions to the birationality of some
pluricanonical map. In particular, apart from a finite list of weighted
baskets, we prove the birationality of , and
respectively.Comment: Final version, 36 pages. Electronic Research Archive (to appear
Unified view of quantum amplification based on quantum transformation
A general framework of quantum state amplification using the language of
quantum state transformation is given systematically for the first time. The
concept of amplification of quantum states is defined specifically and the
amplification of a set of quantum states is formulated generally as the
transformation of quantum states. Three different kinds of important quantum
amplifications, i.e., deterministic noisy quantum amplification, probabilistic
noiseless quantum amplification, and deterministic noiseless quantum
amplification are identified and discussed. For deterministic quan- tum
amplification, the linearity of amplification is proven to be incompatible with
the noiseless amplification while it is not true for probabilistic quantum
amplification. However, deterministic noiseless quantum amplification is shown
physically attainable if the linearity of amplification is given up. The
connection between the gain of amplification and the successful probability is
discussed for probabilistic quantum amplification. Assuming that successful
probability is the same for all quantum states to be amplified, we obtain a
generally valid relation between the gain of amplication and the successful
probability. Particular interest is given to phase-preserving quantum
amplication of Gaussian states which has been shown of theoretical interest and
of practical importance in quantum information and quantum communication
recently. Our results of quantum state amplification not only enrich the
research of quantum amplification but also can be helpful for further practical
applications.Comment: 10 pages, 2 figure
Cascaded Weak Measurements Amplification of Ultra-small Phases
The weak measurements based amplification of ultra-small phase was proposed
in our previous work. Due to the technical imperfections, the ability of
amplification is usually limited in practice. Here we introduce the concept of
cascaded weak measurements amplification so that the ability of weak
measurements amplification can be further improved. A formula of determining
the cascaded number of weak measurements amplification is derived. The method
presented here could be found useful in high precision measurement e.g.,
gravitational waves detection.Comment: Part II of series work. Comments and Suggestions are welcom
Decays of to and
By describing the using the extended Friedrichs scheme, in which
is the dominant component, we calculate the decay rates of the
to and a -wave charmonium state with ,
or , and its decays to where are assumed to
be produced via an intermediate state. The decay widths of
for are of the same order. However, this
model calculation exhibits that the decay rate of to
is one order of magnitude smaller than its decay rate to .Comment: 7 pages, 3 figures; v2, some corrections and minor modification of
the discussion. Final published versio
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